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Compactifications of Symmetric and Locally Symmetric Spaces

Armand Borel Lizhen Ji

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2006 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-8176-3247-2

ISBN electrónico

978-0-8176-4466-6

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Birkhäuser Boston 2006

Cobertura temática

Tabla de contenidos

Introduction

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

- Introduction | Pp. 1-22

Review of Classical Compactifications of Symmetric Spaces

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part I - Compactifications of Riemannian Symmetric Spaces | Pp. 27-105

Uniform Construction of Compactifications of Symmetric Spaces

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part I - Compactifications of Riemannian Symmetric Spaces | Pp. 107-164

Properties of Compactifications of Symmetric Spaces

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part I - Compactifications of Riemannian Symmetric Spaces | Pp. 165-197

Smooth Compactifications of Riemannian Symmetric Spaces

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part II - Smooth Compactifications of Semisimple Symmetric Spaces | Pp. 203-213

Semisimple Symmetric Spaces

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part II - Smooth Compactifications of Semisimple Symmetric Spaces | Pp. 215-219

The Real Points of Complex Symmetric Spaces Defined over ℝ

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part II - Smooth Compactifications of Semisimple Symmetric Spaces | Pp. 221-231

The DeConcini-Procesi Compactification of a Complex Symmetric Space and Its Real Points

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part II - Smooth Compactifications of Semisimple Symmetric Spaces | Pp. 233-247

The Oshima-Sekiguchi Compactification of and Comparison with (ℝ)

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part II - Smooth Compactifications of Semisimple Symmetric Spaces | Pp. 249-262

Classical Compactifications of Locally Symmetric Spaces

Armand Borel; Lizhen Ji

Gene set enrichment analysis is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. In this paper we present a novel method integrating gene interaction information with Gene Ontology (GO) for the construction of new interesting enriched gene sets. The experimental results show that the introduced method improves over traditional methods that compute the enrichment of a single GO terms, i.e. that it is capable to find new statistically relevant descriptions of the biology governing the experiments not detectable by the existing methods.

Part III - Compactifications of Locally Symmetric Spaces | Pp. 267-322